Sound arises from a vibrating body and musical sound results from the interdependency of vibrations or notes as expressed by the existence of overtones and harmonies. The notes used in a musical scale have fixed rates of vibration which are mathematically interrelated.
For historical reasons, the musical alphabet starts from C (not A) and the octave C to C is given the notation C, D, E, F, G, A, B, C, eight notes represented for example by the white keys on a piano keyboard. The octave, "key" or "scale of C major" can also be given an easily singable syllable wherein C, D, E, F, G, A, B, C become doh, ray, me, fah, soh, lah, te, doh. Whether one uses alphabetical symbols C, D, E, etc. or singable symbols doh, ray, me, etc., there is represented an organized system of vibrations that have a definite mathematical relationship.
Although there are five authentic diatonic modes of music, the most familiar modes of music in Western culture are the "major" mode (also known as the Ionian mode) and the "minor mode" (also known as the Aeolian mode) from which major scales and minor scales are derived.
Each mode of music comprises a series of scales known as diatonic scales, one of which is the scale of C major, and each scale comprises a series of seven steps rising from one tone to its octave such as the C to C octave of the C major scale noted above. The steps or intervals between the notes in a scale are either a tone or semi-tone and each mode of music has its own characteristic sequence of tone/semitone steps or intervals between successive notes of its scale.
The tone/semitone relationship is a third way of expressing relationships of note pitch and also may be used to visually express the mathematical relationship of ratios of pitch. A scale has 12 semitones and the arrangement of these tones/semitones holds the key to which scale constitutes either a major or minor mode. (By definition a musical scale is a series of tones arranged in sequence of rising and falling pitches in accordance with any of various systems of intervals).
The major (Ionian) mode of music has a sequence of steps or intervals (using the key of C major as exemplary) of: ##STR1## whereas the minor (Aeolian) mode of music has a sequence of steps or intervals of: ##STR2##
A chord in harmonic music is the simultaneous sounding of tones, usually three or more and in any musical composition, an integral part is the triad chords which are largely responsible for conferring melodic and harmonic characteristics to musical compositions. A triad consists of three notes comprised of alternate notes (e.g. 1, 3 and 5 intervals) of the diatonic scale of the composition within the particular mode of music. The chord is generally referred to by its "base" or lowest note of the chord. For example, in the C major diatonic scale, there are the following (triad) chords:
first--C, E, G; PA1 second--D, F, A; PA1 third--E, G, B; PA1 fourth--F, A, C; PA1 fifth--G, B, D; PA1 sixth--A, C, E; PA1 seventh--B, D, F.
Within the major (mode) Diatonic scales, a triad chord may be a major chord, a minor chord or a diminished chord, the type of chord being determined by the interval of pitch (tone/semitone) between adjacent notes making up the triad chord. The intervals of pitch (tones/semitones) between notes is, as noted above, determined by the mode of music under consideration (e.g. major or minor diatonic scales). Thus whether a triad chord is a major, minor or diminished chord is dependent on the diatonic scale as well as the base note of the chord under consideration.
By way of example, the first triad chord in the C major diatonic scale above is C, E, G (alternate notes) and the tonic intervals (looking at the major tonic scale above) between the alternate notes is respectively 2 tones (C-E) and 11/2 tones (E-G) which are the characteristic intervals of a major chord. Accordingly this C chord is known as C - major chord (in the major diatonic scale). The second triad chord noted above is D, F, A and the tonic intervals are 11/2 tones (D-F) and 2 tones (F-G). This is characteristic of a minor chord (D minor chord in the major diatonic side).
From a review of all of the above Triad chords in conjunction with the major tonic scale above, the following will be noted:
______________________________________ Triad Chord Tonic Separation Chord Characteristic ______________________________________ (1) C, E, G 2 Tones (C-E); Major 11/2 Tones (E-G) (2) D, F, A 11/2 Tones (D-F); Minor 2 Tones (F-A) (3) E, G, B 11/2 Tones (E-G); Minor 2 Tones (G-B) (4) F, A, C 2 Tones (F-A); Major 11/2 Tones (A-C) (5) G, B, D 2 Tones (G-B); Major 11/2 Tones (B-D) (6) A, C, E 11/2 Tones (A-C); Minor 2 Tones (C-E) (7) B, D, F 11/2 Tones (B-D); Diminished 11/2 Tones (D-F) ______________________________________
The chord B, D, F (No.7) has tonic intervals of 11/2 tones and 11/2 tones, characteristic of a diminished chord and is known as the B diminished chord in the C major scale.
Each note of a diatonic scale within a given mode of music can thus be assigned a designation of major, minor or diminished which denotes the character of the triad chord within the mode of music which uses the note as the base note. Since the character of a triad chord indicates its type of structural sound and harmony, a familiarity with the character of chords derived from a given base note in a particular mode of music is helpful in understanding musical structures and making and understanding musical compositions and their melodic forms. Further the chords noted above with "major chord" characteristics of tonic intervals namely the 1st, 4th and 5th chords are known as Prime Chords and they hold many inherent relationships within music.
My earlier U.S. Pat. No. 4,069,735 granted Jan. 24, 1978 provides a teaching and computation device in the form of a slide rule having a base display part with indicia characteristic of different modes of music and includes a second rotatable display part having indicia which can be brought into registry with the indicia on the first part so as to compute chords and scales in any of the presented modes of music. However, such device does not provide a simplified apparatus which includes a representation of a keyboard which is selectively moveable in conjunction with additional indicia on the base display part to interrelate the computational theory with the realities of the keyboard.